Thank you for your caring and your kindness
How do you know the rattie is wild? Is it a roof rat? Do you know if it is a baby, teen or adult?
Do you have pictures you can share?
Many people abandon pet rats outdoors although they are domesticated pets and can not survive in the wild, and sometimes pet rats escape from snake owners.
The rat living in your shed may be a abandoned pet
Some people here in Canada have set up a shed in their yard with bales of straw (not hay). They have put out food and water daily in the shed and the wild mice or rat that were in their home lived happily there. Oxbow and Harlan 2014 are the best blocks for rats. Rats are also fed a variety of daily vegs, grain, etc
A woman I know who has a farm animal rescue and her barns were getting overrun with rats. She used a form of chemical birth control to keep the numbers down. She said that she had done research and that it is safe. She used birth control by SenesTech Inc.
Here is some info that might be helpful:
Strangers in a Strange Land: The case against trapping and relocating - Humane Gardener
You might want to check if there are any good rat rescues in your area in case it is a pet rattie ….... depending on the coloration it may be easy to tell if the rattie is a pet, however, some pet rats have the colouring and appearance of wild rats.
Please let us know what happens and share pictures if possible.